(x+5)(x-2)=4(2x-1)

Solution for (x+5)(x-2)=4(2x-1) equation:

(x+5)(x-2)=4(2x-1)

We move all terms to the left:

(x+5)(x-2)-(4(2x-1))=0

We multiply parentheses ..

(+x^2-2x+5x-10)-(4(2x-1))=0


We calculate terms in parentheses: -(4(2x-1)), so:

4(2x-1)

We multiply parentheses

8x-4

Back to the equation:

-(8x-4)


We get rid of parentheses

x^2-2x+5x-8x-10+4=0

We add all the numbers together, and all the variables

x^2-5x-6=0

a = 1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$